All categories

3 years ago

1. 3x + y = 11 5x - y = 21

Mathematics

1 answer:

sergeinik [125]3 years ago

4 0

Answer:

[4, -1]

Step-by-step explanation:

Using the Elimination Method:

3x + y = 11

5x - y = 21

__________

8x = 32

__ ___

8 8

x = 4 [Plug this back into both equations to get the y-coordinate of -1]; -1 = y

The y's are already additive inverses [result in 0], canceling each other out.

I am joyous to assist you anytime.

You might be interested in

In a Gallup poll, 1025 randomly selected adults were surveyed and 29% of them said that they used the Internet for shopping at l

svetoff [14.1K]

Answer: (0.25,0.33)

Step-by-step explanation:

A 99% confidence interval for population proportion is given by:-

$\hat{p}\pm 2.576\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$ , where $\hat{p}$ = sample proportion, $n$ = sample size.

Given: $n=1025, \hat{p}=0.29$

A 99% confidence interval estimate of the proportion of adults who use the Internet for shopping:

$0.29\pm 2.576\sqrt{\dfrac{0.29(1-0.29)}{1025}}\\\\=0.29\pm 2.576\sqrt{0.00020087804878}\\\\=0.29\pm2.576(0.01417)\\\\=0.29\pm0.03650192\\\\=(0.29-0.03650192,\ 0.29+0.03650192)\\\\=(0.25349808,\ 0.32650192)$

$\approx(0.25,\ 0.33)$

Thus, a 99% confidence interval estimate of the proportion of adults who use the Internet for shopping = (0.25,0.33)

5 0

3 years ago

During it's first 50 days of growth a sunflower grows about 4 cm a day. Using this rate how many days will it take for the sunfl

Alex787 [66]

The answer is 15 days because
$60 \div 4 = 15$

4 0

3 years ago

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

4 0

2 years ago

Write the equation of the line in slope-intercept form that has: slope: -1 and point: (1, 1)

lara31 [8.8K]

Answer:

f(x) = -1x + 1

Step-by-step explanation:

f(x) = mx + b

the equation above is slope intercept form. in order to make it you need a slope and a y intercept. you were given the slope, so now you need a y intercept. but where would you find that??? look no farther than the point you were given, (1,1). the y intercept is the second number in the parentheses. next you take your slope and your y-intercept and place them in.

f(x) = -1x + 1

hope i could help

3 0

2 years ago

¿Cuál es el ángulo complementario de 9°?

Ann [662]

Answer:

90 - 9 = 81°

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers